Question

Find the equation of straight lines which passes through the point (2, – 3) and makes an angle of 45° with line 3x – 2y = 4.

Answer 1

Equation of line passing through point (2, -3)

y + 3 = m₁ (x – 2)

⇒ y = m₁ (x – 2) - 3

⇒ y = m₁ x – (2m₁ + 3)

Eqⁿ of given straight line

3x – 2y = 4

⇒ 2y = 3x – 4

Thus, equation of line

y + 3 = – 5 (x – 2)

⇒ y + 3 + 5(x – 2) = 0

⇒ y + 5x – 7 = 0

Thus, equation of line

y + 3 = 1/5(x – 2)

⇒ 5y + 15 – x + 2 = 0

⇒ 5y – x + 17 = 0

Thus, equation of lines are

y + 5x – 7 = 0 and 5y – x + 17 = 0